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Wide-range semiempirical equations of state of matter for numerical simulation on high-energy processes

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High Temperature Aims and scope

Abstract

An equation of state is a fundamental characteristic of a substance. It is necessary in numerous studies and practically important problems of high energy density physics. In this review, we consider the modern requirements to equations of state, theoretical and experimental methods used to study the thermodynamic properties of a substance, different aspects of constructing wide-range equations of state, and examples of application of wide-range equations of state in simulation of high-energy processes.

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References

  1. Fortov, V.E., Uravneniya sostoyaniya veshchestva ot ideal’nogo gaza do kvark-glyuonnoi plazmy (Equations of State of Matter from an Ideal Gas to a Quark-Gluon Plasma), Moscow: Fizmatlit, 2012.

    Google Scholar 

  2. Fortov, V.E., Ekstremal’nye sostoyaniya veshchestva (Extreme States of Matter), Moscow: Fizmatlit, 2009.

    Google Scholar 

  3. Fortov, V.E., Fizika vysokikh plotnostei energii (Physics of High Energy Densities), Moscow: Fizmatlit, 2013.

    Google Scholar 

  4. Frontiers in High Energy Density Physics, Henderson, D., Ed., Washington: National Research Council, Nat. Acad. Press, 2003.

  5. Hertel, E.S., Bell, R.L., Elrick, M.G., et al., in Shock Waves at Marseille, vol. 1: Hypersonics, Shock Tube, and Shock Tunnel Flow, Brun, R. and Dumitrescu, L.Z., Eds., Berlin: Springer, 1995, p. 377.

  6. Robinson, A., Brunner, T., Carroll, S., et al., Proc. 46th AIAA Aerospace Sciences Meeting and Exhibition, 2008, p. 1235.

    Google Scholar 

  7. Ferrari, A., Dumbser, M., Toro, E.F., and Armanini, A., Comput. Fluids, 2009, vol. 38, no. 6, p. 1203.

    Article  MathSciNet  Google Scholar 

  8. Gasilov, V.A., Boldarev, A.S., D’yachenko, S.V., et al., Mat. Model., 2012, vol. 24, no. 1, p. 44.

    Google Scholar 

  9. Langer, S.H., Karlin, I., and Marinak, M.M., Proc. Int. Conf. on High Performance Computing for Computational Science VECPAR 2014, Cham: Springer, 2014, vol. 8969, p. 173.

    Google Scholar 

  10. Bel’kov, S.A., Bondarenko, S.V., Vergunova, G.A., et al., J. Exp. Theor. Phys., 2017, vol. 124, no. 2, p. 341.

    Article  ADS  Google Scholar 

  11. Landau, L.D. and Lifshits, E.M., Statisticheskaya fizika (Statistical Physics), Moscow: Fizmatlit, 2001.

    MATH  Google Scholar 

  12. Val’ko, V.V., Lomonosov, I.V., Ostrik, A.V., et al., in Fizika yadernogo vzryva (Physics of Nuclear Explosion), 5 vols., vol. 2: Deistvie vzryva (Action of Explosion), Moscow: Fizmatlit, 2010, p. 140.

    Google Scholar 

  13. Lomonosov, I.V., Laser Part. Beams, 2007, vol. 25, no. 04, p. 567.

    Article  Google Scholar 

  14. Tablitsy fizicheskikh velichin. Spravochnik (Tables of Physical Quantities: Reference Book), Kikoin, K.K., Ed., Moscow: Energoatomizdat, 1976.

  15. Gurvich, L.V., Bergman, G.A., Veits, I.V., et al., Termodinamicheskie svoistva individual’nykh veshchestv (Thermodynamic Properties of Individual Substances), 4 vols., Glushko, V.P., Ed., Moscow: Nauka, 1978, 3rd ed.

  16. Fizicheskie velichiny. Spravochnik (Physical Quantities: Reference Book), Grigor’ev, I.S. and Meilikhov, E.Z., Eds., Moscow: Energoatomizdat, 1991.

  17. Jayaraman, A., Rev. Mod. Phys., 1983, vol. 55, p. 65.

    Article  ADS  Google Scholar 

  18. Akahama, Y., Nishimura, M., Kinoshita, K., et al., Phys. Rev. Lett., 2006, vol. 96, 045505.

    Article  ADS  Google Scholar 

  19. Dubrovinsky, L., Dubrovinskaia, N., Prakapenka, V., and Abakumov, A., Nat. Commun., 2012, vol. 3, p. 1163.

    Article  ADS  Google Scholar 

  20. Hanfland, M., Syassen, K., Christensen, N.E., and Novikov, D.L., Nature, 2000, vol. 408, no. 6809, p. 174.

    Article  ADS  Google Scholar 

  21. Tateno, S., Hirose, K., Ohishi, Y., and Tatsumi, Y., Science, 2010, vol. 330, no. 6002, p. 359.

    Article  ADS  Google Scholar 

  22. Boehler, R. and Ross, M., Earth Planet. Sci. Lett., 1997, vol. 153, p. 223.

    Article  ADS  Google Scholar 

  23. Hanstrom, A. and Lazor, P., Earth Planet. Sci. Lett., 2000, vol. 305, p. 209.

    Google Scholar 

  24. Aschcroft, N.W. and Mermin, N.D., Solid State Physics, New York: Holt, Rinehart and Winston, 1976, vol.1.

  25. McMahan, A. and Ross, M., Phys. Rev. B: Solid State, 1977, vol. 15, no. 2, p. 718.

    Article  ADS  Google Scholar 

  26. Ross, M. and Young, D.A., Ann. Rev. Phys. Chem., 1993, vol. 44, p. 61.

    Article  ADS  Google Scholar 

  27. Gillan, M., Alfe, D., Brodholt, J., et al., Rep. Prog. Phys., 2006, vol. 69, no. 8, p. 2365.

    Article  ADS  Google Scholar 

  28. Alfé, D., Comput. Phys. Commun., 2009, vol. 180, no. 12, p. 2622.

    Article  ADS  Google Scholar 

  29. Kohn, W., Rev. Mod. Phys., 1999, vol. 71, no. 5, p. 1253.

    Article  ADS  Google Scholar 

  30. Neaton, J.B. and Ashcroft, N.W., Nature, 1999, vol. 400, no. 6740, p. 141.

    Article  ADS  Google Scholar 

  31. Pickard, C.J. and Needs, R.J., Nat. Mater., 2010, vol. 9, no. 8, p. 624.

    Article  ADS  Google Scholar 

  32. Clérouin, J., Noiret, P., Blottiau, P., et al., Phys. Plasmas, 2012, vol. 19, no. 8, 082702.

    Article  ADS  Google Scholar 

  33. Korobenko, V.N. and Rakhel, A.D., Phys. Rev. B: Condens. Matter Mater. Phys., 2007, vol. 75, no. 6, 064208.

    Article  ADS  Google Scholar 

  34. Lomonosov, I.V. and Gryaznov, V.K., Contrib. Plasma Phys., 2016, vol. 56, nos. 3–4, p. 302

    Article  ADS  Google Scholar 

  35. Zel’dovich, Ya.B. and Raizer, Yu.P., Fizika udarnykh voln i vysokotemperaturnykh gidrodinamicheskikh yavlenii (Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena), Moscow: Fizmatlit, 2008.

    Google Scholar 

  36. Al’tshuler, L.V., Phys.—Usp., 1965, vol. 8, no. 1, p. 52.

    ADS  Google Scholar 

  37. McQueen, R.G., Marsh, SP., Taylor, J.W., et al., in High Velocity Impact Phenomena, Kinslow, R., Ed., New York: Academic, 1970, p. 293, appendices, p. 515.

  38. Compendium of Shock Wave Data (Report UCRL-50108), Van Thiel, M., Ed., Livermore: Lawrence Livermore Lab., 1977.

  39. LASL Shock Hugoniot Data, Marsh, S.P., Berkeley: Univ. of California Press, 1980.

  40. Zhernokletov, M.V., Zubarev, V.N., Trunin, R.F., and Fortov, V.E., Eksperimental’nye dannye po udarnomu szhatiyu i izoentropicheskomu rasshireniyu veshchestv pri vysokikh plotnostyakh energii (Experimental Data on Shock Compression and Isentropic Expansion of Substances at High Energy Densities), Chernogolovka: Inst. Problem Khim. Fiz., Ross. Akad. Nauk, 1996.

    Google Scholar 

  41. Trunin, R.F., Gudarenko, L.F., Zhernokletov, M.V., and Simakov, G.V., Eksperimental’nye dannye po udarno-volnovomu szhatiyu i adiabaticheskomu rasshireniyu kondensirovannykh veshchestv (Experimental Data on Shock-Wave Compression and Adiabatic Expansion of Condensed Matter), Trunin, R.F., Ed., Sarov: Ross. Fed. Yadernyi Tsentr, 2001.

    Google Scholar 

  42. Al’tshuler, L.V. and Bakanova, A.A., Phys.—Usp., 1968, vol. 11, no. 5, p. 678.

    ADS  Google Scholar 

  43. Al’tshuler, L.V., Trunin, R.F., Krupnikov, K.K., and Panov, N.V., Phys.—Usp., 1996, vol. 39, no. 5, p. 539.

    Article  ADS  Google Scholar 

  44. Funtikov, A.I., Phys.—Usp., 1997, vol. 40, no. 10, p. 1067.

    Article  ADS  Google Scholar 

  45. Al’tshuler, L.V., Trunin, R.F., Urlin, V.D., et al., Phys.—Usp., 1999, vol. 42, no. 3, p. 261.

    Article  ADS  Google Scholar 

  46. Fortov, V.E., Phys.—Usp., 2007, vol. 50, no. 4, p. 333.

    Article  ADS  Google Scholar 

  47. Fortov, V.E., Phys.—Usp., 2009, vol. 52, no. 6, p. 615.

    Article  ADS  Google Scholar 

  48. Walsh, J.M., Rice, M.H., McQueen, R.G., and Yarger, F.L., Phys. Rev., 1957, vol. 108, no. 2, p. 196.

    Article  ADS  Google Scholar 

  49. McQueen, R.G. and Marsh, S.P., J. Appl. Phys., 1960, vol. 31, no. 7, p. 1253.

    Article  ADS  Google Scholar 

  50. Al’tshuler, L.V., Krupnikov, K.K., Ledenev, B.N., et al., Zh. Eksp. Teor. Fiz., 1958, vol. 34, p. 874.

    Google Scholar 

  51. Al’tshuler, L.V., Krupnikov, K.K., and Brazhnik, M.I., Zh. Eksp. Teor. Fiz., 1958, vol. 34, p. 886.

    Google Scholar 

  52. Al’tshuler, L.V., Kormer, S.B., and Bakanova, A.A., Zh. Eksp. Teor. Fiz., 1960, vol. 38, p. 790.

    Google Scholar 

  53. Al’tshuler, L.V., Bakanova, A.A., Dudoladov, I.P., et al., J. Appl. Math. Tech. Phys., 1981, vol. 22, no. 2, p. 145.

    Article  ADS  Google Scholar 

  54. Al’tshuler, L.V., Bakanova, A.A., Brazhnik, M.I., et al., Khim. Fiz., 1995, vol. 14, no. 2-3, p. 65.

    Google Scholar 

  55. Trunin, R.F., Panov, N.V, and Medvedev, A.B., Teplofiz. Vys. Temp., 1995, vol. 33, no. 2, p. 329.

    Google Scholar 

  56. Trunin, R.F., Panov, N.V., and Medvedev, A.B., Pis’ma Zh. Eksp. Teor. Fiz., 1995, vol. 62, no. 7, p. 572.

    Google Scholar 

  57. Nikolaev, D., Ternovoi, V., Kim, V., and Shutov, A., J. Phys.: Conf. Ser., 2014, vol. 500, 142026.

    Google Scholar 

  58. Ternovoi, V.Ya., in Dinamika sploshnoi sredy (Dynamics of a Continuous Medium), Novosibirsk: Inst Gidrodin., Sib. Otd., Akad. Nauk SSSR, 1980, no. 48, p. 141.

    Google Scholar 

  59. Jones, A.H., Isbell, W.H., and Maiden, C.J., J. Appl. Phys., 1966, vol. 37, no. 9, p. 3493.

    Article  ADS  Google Scholar 

  60. Al’tshuler, L.V., Moiseev, B.N., Popov, L.V., et al., Zh. Eksp. Teor. Fiz., 1968, vol. 54, no. 3, p. 765.

    Google Scholar 

  61. Trunin, R.F., Podurets, M.A., Moiseev, B.N., et al., Zh. Eksp. Teor. Fiz., 1969, vol. 56, no. 4, p. 1172.

    Google Scholar 

  62. Trunin, R.F., Podurets, M.A., Simakov, G.V., et al., Zh. Eksp. Teor. Fiz., 1972, vol. 62, p. 1043.

    Google Scholar 

  63. Ragan, C.E., Phys. Rev. A: At., Mol., Opt. Phys., 1980, vol. 21, no. 2, p. 458.

    Article  ADS  Google Scholar 

  64. Ragan, C.E., Phys. Rev. A: At., Mol., Opt. Phys., 1982, vol. 25, no. 6, p. 3360.

    Article  ADS  Google Scholar 

  65. Ragan, C.E., Phys. Rev. A: At., Mol., Opt. Phys., 1984, vol. 29, no. 3, p. 1391.

    Article  ADS  Google Scholar 

  66. Vladimirov, A.S., Voloshin, N.P., Nogin, V.N., et al., Pis’ma Zh. Eksp. Teor. Fiz., 1984, vol. 39, p. 69.

    Google Scholar 

  67. Avrorin, E.N., Vodolaga, B.K., Voloshin, N.P., et al., Pis’ma Zh. Eksp. Teor. Fiz., 1986, vol. 43, p. 241.

    Google Scholar 

  68. Avrorin, E.N., Vodolaga, B.K., Voloshin, N.P., et al., Zh. Eksp. Teor. Fiz., 1987, vol. 93, p. 613.

    ADS  Google Scholar 

  69. Ragan, C.E., Silbert, M.G., and Diven, B.C., J. Appl. Phys., 1977, vol. 48, no. 7, p. 2860.

    Article  ADS  Google Scholar 

  70. Volkov, L.P., Voloshin, N.P., Vladimirov, A.S., et al., Pis’ma Zh. Eksp. Teor. Fiz., 1980, vol. 31, p. 623.

    Google Scholar 

  71. Simonenko, V.A., Voloshin, N.P., Vladimirov, A.S., et al., Zh. Eksp. Teor. Fiz., 1985, vol. 88, p. 1452.

    ADS  Google Scholar 

  72. Trunin, R.F., Podurets, M.A., Popov, L.V., et al., Zh. Eksp. Teor. Fiz., 1992, vol. 102, no. 3, p. 1433.

    ADS  Google Scholar 

  73. Trunin, R.F., Podurets, M.A., Popov, L.V., et al., Zh. Eksp. Teor. Fiz., 1993, vol. 103, no. 6, p. 2189.

    Google Scholar 

  74. Anisimov, S.I., Prokhorov, A.M., and Fortov, V.E., Phys.—Usp., 1984, vol. 27, no. 3, p. 181.

    ADS  Google Scholar 

  75. Lindl, J., Landen, O., Edwards, J., and Moses, E., Phys. Plasmas, 2014, vol. 21, no. 2, 020501.

    Article  ADS  Google Scholar 

  76. Löwer, T., Sigel, R., Eidmann, K., et al., Phys. Rev. Lett., 1994, vol. 72, no. 20, p. 3186.

    Article  ADS  Google Scholar 

  77. Cauble, R., Phillion, D.W., Hoover, T.J., et al., Phys. Rev. Lett., 1993, vol. 70, p. 2102.

    Article  ADS  Google Scholar 

  78. Kritcher, A.L., Doeppner, T., Swift, D., et al., J. Phys.: Conf. Ser., 2016, vol. 688, no. 1, 012055.

    Google Scholar 

  79. Al’tshuler, L.P and Petrunin, A.P., Zh. Tekh. Fiz., 1961, vol. 31, p. 717.

    Google Scholar 

  80. Nellis, W.PJ., Moriarty, J.PA., Mitchell, A.PC., et al., Phys. Rev. Lett., 1988, vol. 60, p. 1414.

    Article  ADS  Google Scholar 

  81. Alder, B.J., in Solids under Pressure, Paul, W. and Warschauer, D.M., Eds., New York: McGraw-Hill, 1963, p. 385.

  82. Davis, J.-P., J. Appl. Phys., 2006, vol. 99, 103512.

    Article  ADS  Google Scholar 

  83. Lemke, R.W., Dolan, D.H., Dalton, D.G., et al., J. Appl. Phys., 2016, vol. 119, no. 1, 015904.

    Article  ADS  Google Scholar 

  84. Edwards, J., Lorenz, K.T., Remington, B.A., et al., Phys. Rev. Lett., 2004, vol. 92, 075002.

    Article  ADS  Google Scholar 

  85. Duffy, T.S. and Ahrens, T.J., J. Appl. Phys., 1994, vol. 76, no. 2, p. 835.

    Article  ADS  Google Scholar 

  86. Trunin, R.F., Zhernokletov, M.V., Kuznetsov, N.F., and Shutov, V.V., Teplofiz. Vys. Temp., 1995, vol. 33, no. 2, p. 222.

    Google Scholar 

  87. Krupnikov, K.K., Brazhnik, M.I., and Krupnikova, V.P., Zh. Eksp. Teor. Fiz., 1962, vol. 42, p. 675.

    Google Scholar 

  88. Kormer, S.B., Funtikov, A.I., Urlin, V.D., and Kolesnikova, A.N., Zh. Eksp. Teor. Fiz., 1962, vol. 42, p. 686.

    Google Scholar 

  89. Bakanova, A.A., Dudoladov, I P., and Sutulov, Yu.N., J. Appl. Math. Tech. Phys., 1974, vol. 15, no. 2, p. 241.

    Article  ADS  Google Scholar 

  90. Al’tshuler, L.V., Bushman, A.V., Zhernokletov, M.V., et al., Zh. Eksp. Teor. Fiz., 1980, vol. 78, p. 741.

    Google Scholar 

  91. Trunin, R.F., Simakov, G.V., Sutulov, Yu.N., et al., Zh. Eksp. Teor. Fiz., 1989, vol. 96, p. 1024.

    Google Scholar 

  92. Trunin, R.F., Simakov, G.V., Sutulov, Yu.N., et al., Zh. Eksp. Teor. Fiz., 1989, vol. 95, p. 631.

    ADS  Google Scholar 

  93. Trunin, R.F. and Simakov, G V., Zh. Eksp. Teor. Fiz., 1993, vol. 103, p. 2180.

    Google Scholar 

  94. Gryaznov, V.K., Zhernokletov, M.V., Iosilevskii, I.L., et al., Zh. Eksp. Teor. Fiz., 1998, vol. 114, p. 1242.

    Google Scholar 

  95. Fortov, V.E. and Lomonosov, I.V., Phys.—Usp., 2014, vol. 57, no. 3, p. 219.

    Article  ADS  Google Scholar 

  96. Podurets, A.M., Phys.—Usp., 2011, vol. 54, no. 4, p. 408.

    Article  ADS  Google Scholar 

  97. Osipov, R.S., Funtikov, A.I., and Tsyganov, V.A., High Temp., 1998, vol. 36, no. 4, p. 566.

    Google Scholar 

  98. McQueen, R.G., Fritz, J.N., and Morris, C.E., in Shock Waves in Condensed Matter-83, Asay, J.R., Graham R.A., Straub, G.K., Eds., Elsevier, 1984, p. 95.

  99. Yoo, C.S., Holmes, N.C., Ross, M., et al., Phys. Rev. Lett., 1993, vol. 70, p. 3931.

    Article  ADS  Google Scholar 

  100. Nguyen, J.H. and Holmes, N.C., Nature, 2004, vol. 427, p. 339.

    Article  ADS  Google Scholar 

  101. McWilliams, R.S., Spaulding, D.K., Eggert, J.H., et al., Science, 2012, vol. 338, no. 6112, p. 1330.

    Article  ADS  Google Scholar 

  102. Hixson, R.S., Boness, D.A., Shaner, J.W., and Moriarty, J., Phys. Rev. Lett., 1989, vol. 62, p. 637.

    Article  ADS  Google Scholar 

  103. Al’tshuler, L.V., Bakanova, A.A., Bushman, A.V., et al., Zh. Eksp. Teor. Fiz., 1977, vol. 73, p. 1866.

    Google Scholar 

  104. Ageev, V.G., Bushman, A.V., Kulish, M.I., et al., Pis’ma Zh. Eksp. Teor. Fiz., 1988, vol. 48, p. 608.

    Google Scholar 

  105. Fortov, V.E. and Lomonosov, I.V., Pure Appl. Chem., 1997, vol. 69, p. 893.

    Article  Google Scholar 

  106. Croxton, C.A., Liquid State Physics: A Statistical Mechanical Introduction, Cambridge: Cambridge Univ., 1974.

    Book  Google Scholar 

  107. Sarkisov, G.N., Phys.—Usp., 1999, vol. 42, no. 6, p. 545.

    Article  ADS  Google Scholar 

  108. Car, R. and Parrinello, M., Phys. Rev. Lett., 1985, vol. 55, p. 2471.

    Article  ADS  Google Scholar 

  109. Payne, M.C., Teter, M.P., Allan, D.C., et al., Rev. Mod. Phys., 1992, vol. 64, p. 1045.

    Article  ADS  Google Scholar 

  110. Minakov, D.V., Levashov, P.R., Khishchenko, K.V., and Fortov, V.E., J. Appl. Phys., 2014, vol. 115, no. 22, 223512.

    Article  ADS  Google Scholar 

  111. Minakov, D.V. and Levashov, P.R., Comput. Mater. Sci., 2016, vol. 114, p. 128.

    Article  Google Scholar 

  112. Shpatakovskaya, G.V., Phys.—Usp., 2012, vol. 55, no. 5, p. 429.

    Article  ADS  Google Scholar 

  113. Nikiforov, A.F., Novikov, V.G., and Uvarov, V.B., Kvantovo-statisticheskie modeli vysokotemperaturnoi plazmy i metody rascheta rosselandovykh probegov i uravnenii sostoyaniya (Quantum-Statistical Models of High-Temperature Plasma and Methods for Calculating Rosseland Runs and the Equations of State), Moscow: Fizmatlit, 2000.

    Google Scholar 

  114. Ebeling, W., Forster, A., Fortov, VE., et al., Thermophysical Properties of Hot Dense Plasmas, Stutgart: Teubner, 1991.

    Google Scholar 

  115. Fortov, V.E., Khrapak, A.G., and Yakubov, I.T., Fizika neideal’noi plazmy (Physics of Nonideal Plasma), Moscow: Fizmatlit, 2004.

    Google Scholar 

  116. McQueen, R., in Shock Compression of Condensed Matter-1991, Schmidt, S.C., Dick, R.D., Forbs, J.W., and Tasker, D.G, Eds., Amsterdam: Elsiever, 1992, p. 75.

  117. Boehler, R. and Ramakrishnan, J., J. Geophys. Res., B, 1980, vol. 85, p. 6996.

    Article  ADS  Google Scholar 

  118. Bushman, A.V., Kanel, G.I., Ni, A.L., and Fortov, V.E., Thermophysics and Dynamics of Intense Pulse Loadings, London: Taylor and Fransis, 1993.

    Google Scholar 

  119. Vashchenko, V.Ya. and Zubarev, V.N., Fiz. Tverd. Tela, 1963, vol. 5, p. 886.

    Google Scholar 

  120. Neal, T., Phys. Rev. B: Solid State, 1976, vol. 14, p. 5172.

    Article  ADS  Google Scholar 

  121. Neal, T., in High Pressure Science and Technology, Timmerhaus, K.D. and Barber, M.S., Eds., New York: Plenum, 1979, vol. 1, p. 80.

    Article  Google Scholar 

  122. Romain, J.P., Migault, A., and Jacquesson, J., J. Phys. Chem. Solids, 1980, vol. 41, p. 323.

    Article  ADS  Google Scholar 

  123. Kormer, S.B., Urlin, V.D., and Popova, L.T., Fiz. Tverd. Tela, 1961, vol. 3, p. 2131.

    Google Scholar 

  124. Kuropatenko, V.F. and Minaeva, I.S., Chisl. Metody Mekh. Sploshnoi Sredy, 1982, vol. 13, no. 6, p. 69.

    Google Scholar 

  125. Birch, F., Phys. Rev., 1947, vol. 71, p. 809.

    Article  ADS  Google Scholar 

  126. Morse, P.M., Phys. Rev., 1929, vol. 34, p. 57.

    Article  ADS  Google Scholar 

  127. Anderson, O.L., Equations of state of solids for geophysics and ceramic science, Oxford Monographs on Geology and Geophysics, Oxford: Oxford University Press, 1995, no.31.

  128. Vinet, P., Ferrante, J., Smith, J.R., and Rose, J.H., J. Phys. C: Solid State Phys., 1986, vol. 19, no. 20, p. L467.

    Article  ADS  Google Scholar 

  129. Holzapfel, W.B., Rep. Prog. Phys., 1996, vol. 59, no. 1, p. 29.

    Article  ADS  Google Scholar 

  130. Romain, J.P., Migault, A., and Jacquesson, J., J. Phys. Chem. Solids, 1976, vol. 37, p. 1159.

    Article  ADS  Google Scholar 

  131. Bushman, A.V., Lomonosov, I.V., and Fortov, V.E., Uravneniya sostoyaniya metallov pri vysokikh plotnostyakh energii (Equations of State of Metals at High Energy Densities), Chernogolovka: Inst. Problem Khim. Fiz., Ross. Akad. Nauk, 1992.

    Google Scholar 

  132. Kalitkin, N.N. and Govorukhina, I.A., Fiz. Tverd. Tela, 1965, vol. 7, p. 355.

    Google Scholar 

  133. Kalitkin, N.N. and Kuz’mina, L.V., Tables of thermodynamic functions of matter at a high energy concentration, Preprint of the Inst. of Applied Mathematics, USSR Acad. Sci., Moscow, 1975, no.35.

  134. Gasnier, R., in Proc. Simposium HDP, Paris: Dunod, 1968.

    Google Scholar 

  135. Pastine, D.J. and Carrol, M.J., in Accurate Characterization of the High Pressure Environment, Lloyd, E.C., Ed., Washington, DC: U.S. Government Printing Office, 1971, p. 91.

  136. Grover, R., J. Chem. Phys., 1971, vol. 55, p. 3435.

    Article  ADS  Google Scholar 

  137. Grover, R., in Proc. Seventh Simposium on Thermophysical Properties, Cezairliyan, A., Ed. New York: ASME, 1977, p. 67.

  138. Grover, R., in High Pressure Science and Technology, Timmerhaus, K.D., Barber, M.S, Eds., New York: Plenum, 1979, vol. 1, p. 33.

    Article  Google Scholar 

  139. Naumann, R.G., J. Appl. Phys., 1971, vol. 42, no. 12, p. 4945.

    Article  ADS  Google Scholar 

  140. Urlin, V.D., Zh. Eksp. Teor. Fiz., 1965, vol. 49, p. 485.

    Google Scholar 

  141. Sapozhnikov, A.T. and Pershina, A.V., Vopr. At. Nauki Tekh., Ser.: Metod. Progr. Chisl. Resheniya Zadach Mat. Fiz., 1979, vol. 3, no. 4, p. 47.

    Google Scholar 

  142. Carter, W.J., Fritz, J.N., Marsh, S.P., and McQueen, R.G., J. Phys. Chem. Solids, 1975, vol. 36, nos. 7–8, p. 741

    Article  ADS  Google Scholar 

  143. Vorob’ev, V.S., Teplofiz. Vys. Temp., 1995, vol. 33, no. 4, p. 557.

    Google Scholar 

  144. Young, D.A. and Alder, B.J., Phys. Rev. A: At., Mol., Opt. Phys., 1971, vol. 3, p. 364.

    Article  ADS  Google Scholar 

  145. Kerley, G.I., Int. J. Impact Eng., 1987, vol. 5, nos. 1–4, p. 441

    Article  Google Scholar 

  146. Medvedev, A.B., Vopr. At. Nauki Tekh., Ser.: Teor. Prikl. Fiz., 1992, vol. 26, no. 1, p. 23.

    Google Scholar 

  147. Medvedev, A.B. and Trunin, R.F., Phys.—Usp., 2012, vol. 55, no. 8, p. 773.

    Article  Google Scholar 

  148. Voropinov, A.I., Gandel’man, G.M., and Podval’nyi, V.G., Phys.—Usp., 1970, vol. 13, no. 1, p. 56.

    ADS  Google Scholar 

  149. Maksimov, E.G., Magnitskaya, M.V., and Fortov, V.E., Phys.—Usp., 2005, vol. 48, no. 8, p. 780.

    Article  Google Scholar 

  150. Godwal, B.K., Sikka, S.K., and Chidambaram, R., Phys. Rev. B: Condens. Matter Mater. Phys., 1979, vol. 20, p. 2362.

    Article  ADS  Google Scholar 

  151. Kinelovskii, S.A. and Maevskii, K.K., High Temp., 2014, vol. 52, no. 6, p. 821.

    Article  Google Scholar 

  152. Kinelovskii, S.A. and Maevskii, K.K., High Temp., 2016, vol. 54, no. 5, p. 675.

    Article  Google Scholar 

  153. Kerley, G., Multiphase equation of state for iron, Report no. SAND93–0027, Albuquerque: Sandia Natl. Labs., 1993.

    Google Scholar 

  154. Liberman, D.A., Phys. Rev. B: Condens. Matter Mater. Phys., 1979, vol. 20, p. 4981.

    Article  ADS  Google Scholar 

  155. Kerley, G.I., User’s manual for Panda II: A computer Code for Calculating Equations of state, Report no. SAND88-2291, Albuquerque: Sandia Natl. Labs., 1991.

    Google Scholar 

  156. More, R.M., Warren, K.H., Young, D.A., and Zimmerman, G.B., Phys. Fluids, 1988, vol. 31, p. 3059.

    Article  ADS  Google Scholar 

  157. Young, D.A. and Corey, E.M., J. Appl. Phys., 1995, vol. 78, no. 6, p. 3748.

    Article  ADS  Google Scholar 

  158. Basko, M.M., Teplofiz. Vys. Temp., 1985, vol. 23, no. 5, p. 483.

    Google Scholar 

  159. Kormer, S.B., Sinitsyn, M.V., Kirillov, G., and Urlin, V.D., Zh. Eksp. Teor. Fiz., 1965, vol. 48, p. 1033.

    Google Scholar 

  160. Ross, M., Phys. Rev., 1968, vol. 171, p. 777.

    Article  ADS  Google Scholar 

  161. Khishchenko, K.V., Lomonosov, I.V., Fortov, V.E., and Shlenskii, O.F., Phys.–Dokl., 1996, vol. 41, no. 7, p. 304.

    ADS  Google Scholar 

  162. Khishchenko, K.V., High Temp., 1997, vol. 35, no. 6, p. 991.

    Google Scholar 

  163. Fortov, V.E. and Lomonosov, I.V., Open Plasma Phys. J., 2010, vol. 3, p. 122.

    Article  ADS  Google Scholar 

  164. Kovalenko, G.V. and Sapozhnikov, A.T., Vopr. At. Nauki Tekh., Ser.: Metod. Progr. Chisl. Resheniya Zadach Mat. Fiz., 1979, vol. 3, no. 4, p. 40.

    Google Scholar 

  165. Lyon, S.P. and Johnson, J.D., SESAME: The Los Alamos national laboratory equation of state database, Report no. LA-UR-92-3407, Los Alamos: Los Alamos National Lab., 1995.

    Google Scholar 

  166. Trainor, K.S., J. Appl. Phys., 1983, vol. 54, no. 5, p. 2372.

    Article  ADS  Google Scholar 

  167. Young, D.A., Wolford, J.K., Rogers, F.J., and Holian, K.S., Phys. Lett. A, 1985, vol. 108, no. 3, p. 157.

    Article  ADS  Google Scholar 

  168. Young, D., Soft-sphere model for liquid metals, Report no. UCRL-52352, Livermore: Lawrence Livermore Lab., 1977.

    Book  Google Scholar 

  169. Holian, K.S., J. Appl. Phys., 1986, vol. 59, no. 1, p. 149.

    Article  ADS  MathSciNet  Google Scholar 

  170. Sjostrom, T., Crockett, S., and Rudin, S., Phys. Rev. B: Condens. Matter Mater. Phys., 2016, vol. 94, 144101.

    Article  ADS  Google Scholar 

  171. Johnson, J.D., High Pressure Res., 1991, vol. 6, no. 5, p. 277.

    Article  ADS  Google Scholar 

  172. Chisolm, E.D., Thomas–Fermi–Dirac theory as calculated in the EOS-production programs Grizzly and Opensesame, Report no. LA-UR-05-2297, Los Alamos: Los Alamos National Lab., 2003.

    Google Scholar 

  173. Bushman, A.V., Efremov, V P., Lomonosov, I.V., et al., Teplofiz. Vys. Temp., 1990, vol. 28, no. 6, p. 1232.

    Google Scholar 

  174. Bushman, A.V., Efremov, V.P., Kanel’, G.I., et al., Khim. Fiz., 1992, vol. 11, no. 3, p. 410.

    Google Scholar 

  175. Bushman, A.V., Lomonosov, I.V., and Fortov, V.E., Sov. Technol. Rev., Sec. B: Thermal Phys., 1993, vol. 5, no. 1, p. 1.

    Google Scholar 

  176. Bushman, A.V., Zhernokletov, M.V., Lomonosov, I.V., et al., Pis’ma Zh. Eksp. Teor. Fiz., 1993, vol. 58, no. 8, p. 640.

    Google Scholar 

  177. Bushman, A.V., Zhernokletov, M.V., Lomonosov, I.V., et al., Dokl. Akad. Nauk, 1993, vol. 329, no. 5, p. 581.

    Google Scholar 

  178. Bushman, A.V., Lomonosov, I.V., Fortov, V.E., and Khishchenko, K.V., Khim. Fiz., 1994, vol. 13, no. 1, p. 64.

    Google Scholar 

  179. Bushman, A.V., Lomonosov, I.V., Fortov, V.E., and Khishchenko, K.V., Khim. Fiz., 1994, vol. 13, no. 5, p. 97.

    Google Scholar 

  180. Lomonosov, I.V., Fortov, V.E., and Khishchenko, K.V., Khim. Fiz., 1995, vol. 14, no. 1, p. 47.

    Google Scholar 

  181. Bushman, A.V., Zhernokletov, M.V., Lomonosov, I.V., et al., Zh. Eksp. Teor. Fiz., 1993, vol.109.

  182. Khishchenko, K.V., Zhernokletov, M.V., Lomonosov, I.V., and Sutulov, Yu.N., Tech. Phys., 2005, vol. 50, no. 2, p. 197.

    Article  Google Scholar 

  183. Barysheva, N.M., Zherebtsov, V.A., and Sin’ko, G.A., Vopr. At. Nauki Tekh., Ser.: Metod. Progr. Chisl. Resheniya Zadach Mat. Fiz., 1988, vol. 15, no. 2, p. 80.

    Google Scholar 

  184. Sin’ko, G.V., Teplofiz. Vys. Temp., 1983, vol. 21, p. 1041.

    Google Scholar 

  185. Fortov, V.E., J. Appl. Math. Tech. Phys., 1972, vol. 13, no. 6, p. 894.

    Article  ADS  Google Scholar 

  186. NIST Standard Reference Data. https://www.nist.gov/srd.

  187. Belov, GV., Iorish, VS., and Yungman, V.S., CALPHAD: Comput. Coupling Phase Diagrams Thermochem., 1999, vol. 23, no. 2, p. 173.

    Article  Google Scholar 

  188. Belov, G.V., Iorish, V.S., and Yungman, V.S., High Temp., 2000, vol. 38, no. 2, p. 191.

    Article  Google Scholar 

  189. Osina, E.L. and Gusarov, A.V., High Temp., 2015, vol. 53, no. 6, p. 817.

    Article  Google Scholar 

  190. Gusarov, A.V., High Temp., 2016, vol. 54, no. 5, p. 771.

    Article  Google Scholar 

  191. Levashov, P.R., Khishchenko, K.V., Lomonosov, I.V., and Fortov, V.E., in Shock Compression of Condensed Matter-2003 (AIP Conf. Proc. 706), Furnish, M.D., Gupta, Y.M., and Forbes, J.W., Eds., 2004, vol. 706, p. 87.

    Article  ADS  Google Scholar 

  192. Fortov, V.E., Goel, B., Munz, C.-D., et al., Nucl. Sci. Eng., 1996, vol. 123, no. 2, p. 169.

    Article  Google Scholar 

  193. Fortov, V.E., Kim, V.V., Lomonosov, I.V., et al., Int. J. Impact Eng., 2006, vol. 33, nos. 1–12, p. 244

    Article  Google Scholar 

  194. Povarnitsyn, M.E., Khishchenko, K.V., and Levashov, P.R., Int. J. Impact Eng., 2008, vol. 35, no. 12, p. 1723.

    Article  Google Scholar 

  195. Povarnitsyn, M.E., Zakharenkov, A.S., Levashov, P.R., and Khishchenko, K.V., Vychisl. Metody Program., 2012, vol. 13, p. 424.

    Google Scholar 

  196. Fortova, S.V., Kraginskii, L.M., Chikitkin, A.V., and Oparina, E.I., Mat. Model., 2013, vol. 25, no. 5, p. 123.

    Google Scholar 

  197. Belotserkovskaya, M.S., Pronina, A.P., Fortova, S.V., and Shepelev, V.V., Comput. Math. Math. Phys., 2016, vol. 56, no. 6, p. 1185.

    Google Scholar 

  198. Belotserkovskii, O.M., Fortova, S.V., Troshkin, O.V., et al., Mat. Model., 2016, vol. 28, no. 2, p. 19.

    MathSciNet  Google Scholar 

  199. Yakovlev, I.V., Combust., Explos. Shock Waves (Engl. Transl.), 1973, vol. 9, no. 3, p. 390.

    Article  Google Scholar 

  200. Liquornik, D.J., Digitized data for Delco test 4007, lead-on-lead, Report no. DDV-86-0010, Livermore: Lawrence Livermore Lab, 1986.

    Google Scholar 

  201. Mullin, S.A., Chhabildas, L.C., and Piekutowski, A.J., in High-Pressure Science and Technology-1993, Schmidt, S.C., Shaner, J.W., Samara, G.A., and Ross, M., New York: AIP, 1994, p. 1817.

  202. Kanel’, G.I., Razorenov, S.V., Utkin, A.V., and Fortov, V.E., Eksperimental’nye profili udarnykh voln v kondensirovannykh sredakh (Experimental Shock Wave Profiles in Condensed Media), Moscow: Fizmatlit, 1996.

    Google Scholar 

  203. Holian, K.S., Int. J. Impact Eng., 1990, vol. 10, nos. 1–4, p. 231

    Article  Google Scholar 

  204. Tahir, N.A., Kain, V., Schmidt, R., et al., Phys. Rev. Lett., 2005, vol. 94, no. 13, 135004.

    Article  ADS  Google Scholar 

  205. Tahir, N.A., Deutsch, C., Fortov, V.E., et al., Phys. Rev. Lett., 2005, vol. 95, 035001.

    Article  ADS  Google Scholar 

  206. Varentsov, D., Ternovoi, V.Y., Kulish, M., et al., Nucl. Instrum. Methods Phys. Res., Sect. A, 2007, vol. 577, nos. 1–2, p. 262

    Article  ADS  Google Scholar 

  207. Tahir, N.A., Piriz, A.R., Shutov, A., et al., Contrib. Plasma Phys., 2007, vol. 47, nos. 4–5, p. 223

    Article  ADS  Google Scholar 

  208. Tahir, N.A., Schmidt, R., Brugger, M., et al., Laser Part. Beams, 2007, vol. 25, no. 4, p. 639.

    Google Scholar 

  209. Tahir, N.A., Kim, V.V., Matvechev, A.V., et al., Laser Part. Beams, 2008, vol. 26, no. 2, p. 273.

    Article  Google Scholar 

  210. Tahir, N.A., Matveichev, A., Kim, V., et al., Laser Part. Beams, 2009, vol. 27, no. 1, p. 9.

    Article  ADS  Google Scholar 

  211. Tahir, N.A., Schmidt, R., Shutov, A., et al., Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2009, vol. 79, no. 4, 046410.

    Article  Google Scholar 

  212. Tahir, N.A., Schmidt, R., Brugger, M., et al., Phys. Plasmas, 2009, vol. 16, no. 8, 082703.

    Article  ADS  Google Scholar 

  213. Tahir, N.A., Stoehlker, T., Shutov, A., et al., New J. Phys., 2010, vol. 12, 073022.

    Article  ADS  Google Scholar 

  214. Tahir, N.A., Schmidt, R., Shutov, A., et al., Contrib. Plasma Phys., 2011, vol. 51, no. 4, p. 299.

    Article  ADS  Google Scholar 

  215. Tahir, N.A., Kim, V., Lamour, E., et al., Nucl. Instrum. Methods Phys. Res., Sect. B, 2012, vol. 276, p. 66.

    Article  ADS  Google Scholar 

  216. Tahir, N.A., Kim, V., Lamour, E., et al., Nucl. Instrum. Methods Phys. Res., Sect. B, 2012, vol. 290, p. 43.

    Article  ADS  Google Scholar 

  217. Tahir, N.A., Kim, V., Schlitt, B., et al., Phys. Rev. Spec. Top.–Accel. Beams, 2014, vol. 17, no. 4, 041003.

    Article  ADS  Google Scholar 

  218. Mintsev, V., Kim, V., Lomonosov, I., et al., Contrib. Plasma Phys., 2016, vol. 56, nos. 3–4, p. 281

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Institute of Problems of Chemical Physics, Russian Academy of Sciences, Chernogolovka, Moscow oblast, 142432, Russia

    I. V. Lomonosov

  2. Tomsk State University, Tomsk, 634050, Russia

    I. V. Lomonosov

  3. Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow, 125412, Russia

    I. V. Lomonosov

  4. Moscow Institute of Physics and Technology, State University, Dolgoprudny, Moscow oblast, 141701, Russia

    I. V. Lomonosov

  5. Lomonosov Moscow State University, Moscow, 119991, Russia

    I. V. Lomonosov

  6. Institute of Computer Aided Design, Russian Academy of Sciences, Moscow, 123056, Russia

    S. V. Fortova

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  1. I. V. Lomonosov
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Original Russian Text © I.V. Lomonosov, S.V. Fortova, 2017, published in Teplofizika Vysokikh Temperatur, 2017, Vol. 55, No. 4, pp. 596–626.

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Lomonosov, I.V., Fortova, S.V. Wide-range semiempirical equations of state of matter for numerical simulation on high-energy processes. High Temp 55, 585–610 (2017). https://doi.org/10.1134/S0018151X17040113

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